Method of analysis of samples by determination of a function of specific brightness

ABSTRACT

A method for characterizing samples having units, by monitoring fluctuating intensities of radiation emitted, scattered and/or reflected by said units in at least one measurement volume, the monitoring being performed by at least one detection means, said method comprising the steps of:  
     a) measuring in a repetitive mode a number of photon counts per time interval of defined length,  
     b) determining a function of the number of photon counts per said time interval,  
     c) determining a function of specific brightness of said units on basis of said function of the number of photon counts.

[0001] The present invention relates to a method for characterizingsamples having units which emit, scatter and/or reflect radiation bymeasuring in a repetitive mode a number of photon counts per timeinterval of defined length and determining a function of the number ofphoton counts.

[0002] The first successful studies on fluorescence intensityfluctuations were performed by Magde, Elson and Webb (Biopolymers, Vol.13, 29-61, 1974) who demonstrated the possibility to detect numberfluctuations of fluorescent molecules and established a research fieldcalled fluorescence correlation spectroscopy (FCS). FCS was primarilydeveloped as a method for determining chemical kinetic constants anddiffusion coefficients. The experiment consists essentially in measuringthe variation with time of the number of molecules of specific reactantsin a defined open volume of solution. The concentration of a reactant ismeasured by its fluorescence from a small measurement volume. Themeasurement volume is defined by a focussed laser beam, which excitesthe fluorescence, and a pinhole in the image plane of the microscopecollecting fluorescence. Intensity of fluorescence emission fluctuatesin proportion with the changes in the number of fluorescent molecules asthey diffuse into and out of the measurement volume and as they arecreated or eliminated by the chemical reactions. Technically, the directoutcome of an FCS experiment is the calculated autocorrelation functionof the measured fluorescence intensity.

[0003] An important application of FCS is determination ofconcentrations of fluorescent species having different diffusion rates,in their mixture. In order to separate the two terms in theautocorrelation function of fluorescence intensity corresponding totranslation diffusion of two kinds of particles, at least about atwo-fold difference in diffusion time is needed, which corresponds to aneight-fold mass difference of particles. Furthermore, even if onesucceeds in separating the two terms in the autocorrelation function offluorescence intensity, it is yet not sufficient for determining thecorresponding concentrations except if one knows the relative brightnessof the two different types of particles.

[0004] Whereas conventional FCS yields rather limited information aboutaggregate sizes from a simple autocorrelation function of fluorescenceintensity fluctuations, possible biophysical applications demand theability to analyse complex mixtures of different species. For thatpurpose, Palmer and Thompson studied higher order correlation functionsof fluorescence intensity fluctuations and have outlined methods fordetermining the number densities and relative molecular brightness offluorescence of different fluorescent species (Biophys. J., Vol. 52,257-270, August 1987). Their technique may in principle proof useful indetecting and characterizing aggregates of fluorescent-labeledbiological molecules such as cell surface receptors, but has a majordisadvantage of being rather complex, so that data processing of anexperiment including the calculation of high-order correlation functionslasts hours.

[0005] A considerably less complicated method than calculation of highorder auto-correlation functions for characterizing mixtures offluorescent species of different specific brightness is calculation ofhigher order moments of fluorescence intensity out of the experimentallydetermined distribution of the number of photon counts. This method waspresented by Qian and Elson (Biophys. J., Vol. 57, 375-380, February1990; Proc. Natl. Acad. Sci. USA, Vol. 87, 5479-5483, July 1990,). Intheir demonstration experiments signal acquisition times of about 7minutes were used for a relatively favourable experimental system of twokinds of fluorescent particles which differed by 30-fold in theirspecific brightness, the mixture of monomers and 30-mers. The method ofmoments is relatively simple and fast in calculations, but it allows todetermine only a limited number of unknown parameters characterizing thesample because usually only about three or four first moments offluorescence intensity can be calculated from the experiment withprecision sufficient for further analysis.

[0006] Because of this reason, the method of moments is hardly suitablefor characterizing complex samples or selecting between competing modelsof the sample or checking whether the given model is appropriate.

[0007] One object of the invention is to obtain reliable informationabout a sample having units emitting, scattering and/or reflectingphotons, which renders possible an analysis of the sample wish respectto certain ingredients or with respect to certain states of the sample.

[0008] Another object of the present invention is to substantiallyextend the useful information obtainable from the experimentallydetermined function, preferably distribution of the number of photoncounts.

[0009] The objects of the present invention are solved with the methodhaving the features of claim 1.

[0010] The term “unit of a sample” refers, in general, to subparts ofthe sample which are capable of emitting, scattering and/or reflectingradiation. A sample might contain a number of identical units ordifferent units which preferably can be grouped into species. The term“different species” refers also to different states, in particulardifferent conformational states, of a unit such as a molecule.Fluorescently labelled or naturally fluorescent molecules, molecularcomplexes, vesicles, cells, beads and other particles in water or otherliquids are examples of fluorescent units in liquid samples, whileexamples of fluorescent units of a solid sample are impurity molecules,atoms or ions, or other fluorescence centers.

[0011] What is meant by the term “specific brightness” of units in thesense of the present invention is a physical characteristic expressingin what extent a unit of given species is able to emit, scatter and/orreflect radiation, preferably light. It is thought to characterizesingle units, preferably particles, and therefore the value of specificbrightness is not depending on concentration of the units, neither onthe presence of other units. Thus, a change of the total count rate ofphotons emitted, scattered and/or reflected from the measurement volume,if only due to a change in concentration of the total number of units,does not influence the measured value of specific brightness and thevalue of the ratio of numbers of units of different species determinedby the present invention. Specific brightness is usually expressed interms of the mean count rate per unit which is a weighted average of thecount rate over coordinates of the unit in the measurement volume. Insome cases, one might prefer to express specific brightness in countrates corresponding to a unit positioned in a place where the count ratehas its top values. This could e.g. be the center of the focus of anincident beam.

[0012] The importance of the present invention for the analysis ofsamples may be illustrated by the following, non-limiting example:Assuming that a solution contains a quantity (a) of one type ofparticles (A) with a respective specific brightness (Ia) and a quantity(b) of another type of particles (B) with a respective specificbrightness (Ib), the overall count rate of photons emitted by thesolution depends on the expression Ia*a-Ib*b. Thus, by meredetermination of the overall count rate, it is not possible to dissolvethe value of a and/or b. Generally, in fluorimetric measurements, theoverall count rate of at least one type of particles is determined in anindependent experiment. If the total number a+b of particles does notchange with respect to this measurement, the ratio a/b or its inversecan be determined by mere determination of the overall count rate of themixture in a second measurement. However, the assumption, that the totalnumber a+b does not change between the two measurements, is often wrong.For example, adsorption effects of particles to surfaces may occur.Fluorimetric measurements cannot verify the total number of particlesa+b independently. The present invention overcomes these restrictions.From one measurement, the numbers of particles a and b can be determinedwithout any prior information of their respective specific brightnesses.

[0013] It is to be understood that the following description is intendedto be illustrative and not restrictive. Many embodiments will beapparent to those of skill in the art upon reviewing the followingdescription. By way of example, the invention will be describedprimarily with reference to measuring numbers of photon counts fromlight emitted by fluorescently labelled particles in a sample. Forexample, in some embodiments it may be desirable to measure numbers ofphoton counts of other origin than fluorescence.

[0014] The present invention provides a method for calculating theexpected function, preferably the distribution of the number of photoncounts corresponding to given real equipment and samples of givencomposition. The ability to predict the distribution of the number ofcounts corresponding to samples to given composition allows, whenstudying samples of unknown composition, to find out the model of thesample yielding the closest fit between the calculated and theexperimentally determined distribution of the number of photon counts.What is meant by the composition of the sample here is the specificbrightness and concentration of units present in the sample. Forexample, a solution of a single fluorescent dye is characterized by twoparameters: the concentration and specific brightness of the dyemolecules. A mixture of two fluorescent dyes is characterized by fourparameters: the concentrations and specific brightnesses of the two kindof molecules. A complex mixture can be characterized by the distributionfunction of concentration versus specific brightness of molecules.Conveniently, concentration is expressed as the mean number of units permeasurement volume, and specific brightness is expressed as the meancount rate per unit. Preferably said units are particles.

[0015] From the other side, the function, e.g. the distribution of thenumber of photon counts depends not only on composition of the sample,but also on equipment: first of all, on the spatial brightness functioncharacteristic to the optical set-up, and on some characteristics of thedetector like its dark count rate, its dead time and probability ofafterpulsing. In the interest of a high quality of analysis, which isindicated by achieving a close fit between the experimentally determinedand the calculated curves, it is preferred to characterize the equipmentadequately.

[0016] Claim 1 does not cover the method described by Qian and Elson, astheir method compares estimated and calculated moments of thedistribution of light intensity, but not directly the distribution ofthe number of photon counts. Qian and Elson's teaching misses theteaching of the present invention.

[0017] According to the invention, a new quality of analysis of samplescontaining units, preferably particles, which emit, scatter and/orreflect radiation, preferably light, becomes possible. In a first step,a number of photon counts from radiation emitted, scattered and/orreflected by the units in the sample is measured per time interval ofdefined length in a repetitive mode. A series of different timeintervals can also be used for a more complex analysis. In step 1, thenumber of photon counts is measured in a repetitive mode, i.e. thenumber of detected photons is counted preferably many times, repeatingthe procedure in a series of preferably consecutive time intervals, inorder to obtain statistically meaningful data. The length of the timeinterval is the duration of the time interval during which the number ofphoton counts is determined. The length of the time interval is usuallyexpressed in microseconds or milliseconds or other units of time.

[0018] In a second step of the method according to the invention, afunction, preferably a distribution of the number of photon counts persaid time interval is determined, which means that it is determined howmany times one has obtained a certain number of photon counts. Thedistribution is a function of the number of photon counts, expressingeither the relative or absolute number of observed (or expected) eventswhen a particular number of photon counts was (or is) obtained.

[0019] In a third step, the experimentally determined distribution ofphoton counts is analyzed directly without intermediate steps to obtaina function, preferably a distribution of specific brightnesses of theunits in the sample.

[0020] It is preferred that at least one detection means monitors saidnumber of photon counts. Any detector which is capable to detectradiation emitted, scattered and/or reflected by units of the sample maybe used, said radiation arising preferably out of at least onemeasurement volume. Appropriate detection means such as an avalanchephoto-diode, a photomultiplier or conventional photo-diodes are wellknown to those of skill in the art. It might also be preferred to use amultidetector consisting of a monolithic configuration of a plurality todetectors, especially if one wants to measure a set of samples inparallel as it is the case in miniaturized high throughput screening. Itmight further be preferred to use a two-dimensional multi-arraydetector.

[0021] In the sense of the present invention, particles are preferablyluminescently labelled or unlabelled, preferably naturally luminescent,molecules or macromolecules, or dye molecules, molecular aggregates,complexes, vesicles, cells, viruses, bacteria, beads, or mixturesthereof.

[0022] The luminescence properties of the units can be varied byconjugating them with a specific luminophore via different linkermolecules. It might be preferred to use polymeric linker moleculesconsisting of a varying number of equal or different monomers.

[0023] It may be advantageous to provide at least one of the units witha specific site to which an affinity substance having detectableproperties will bind.

[0024] In a preferred embodiment, at least one of the units has a tag ofhistidine residues to which an affinity substance such as a chelatecomplex can bind. It might be preferred to use complexes ofnickel-nitrilotriacetic acid (Ni-NTA) and a luminescence label as saidaffinity substance. In a further preferred embodiment, said complexcontains two or more chelating groups and at least one luminescencelabel.

[0025] The luminescence properties of the units may also be varied byconjugating them with a first molecule, as e.g. biotin, which binds aluminescently labelled second molecule, as e.g. luminescently labelledavidin or streptavidin, or vice versa as it is described in detail inexample 3.

[0026] Luminescence properties of a unit can also be changed by energytransfer. Energy absorbed by a donor is transferred upon close contactto a luminophore of an acceptor and subsequently emitted.

[0027] In a further preferred embodiment, the units, preferablyparticles, each carry a number of binding sites for luminescentparticles. Luminescent particles can directly or via secondary moleculesbind to these binding sites. Since highly luminescent particles aregenerated when many luminescent particles bind to the binding sites ofthe first particles, the method according to the invention is able todistinguish easily between particles with a large difference inluminescence intensity, so that even a small amount of bound luminescentparticles can be measured in presence of an excess concentration of freeluminescent particles. This embodiment provides a new analysis ofparticles which do not carry a luminescent label by binding to a secondparticle which is luminescently labelled, but whose brightness does notchange upon binding. A commercially very important application of thismethod is the measurement of fluorescently labelled antibodies bindingto an antigen, while the antigen is binding to at least one of themultiple binding sites of the particle which is preferably a bead, orvice versa. The method can also be applied to other types ofinteractions such as nucleic acid hybridization or protein/nucleic acidinteraction. The invention can also be applied for the analysis ofdistribution characteristics of said particles, such as for qualitycontrol and process control of polymers or oligomeric suspensions ofparticles. In addition, surface areas of particles can be analyzed aswell as distributions of surface areas of particles.

[0028] In a preferred embodiment, one type of particle, subsequentlydenoted A, carries more than one binding site. Another, luminescent typeof particles, subsequently denoted C, can bind (i) either directly to atleast one of the binding sites of particle A, or (ii) binds to at leastone binding site of a molecule B, which in turn binds to at least one ofthe binding sites of particle A. These bindings may be mediated eitherby naturally occurring binding sites on the particles, or mediated byintroduction of specific binding sites to the particles A, B and/or C.Since in both cases more than one of the particles of type C may band toparticle A, the complex will emit more photons than free particles oftype C. This embodiment provides a convenient way to measure binding ofparticles of type B to a particle of type C or A, although the particleof type B is not luminescently labelled.

[0029] In a further preferred embodiment, the measurement volume is onlya part of the total volume of the sample and said units, preferablyparticles, are diffusing and/or being actively transported into and outof said measurement volume and/or the sample is actively transportedand/or optically scanned. If said units, e.g. fluorescent particles, aresufficiently small, then diffusion is fast enough for data acquisitionfrom a great number of independent measurement volumes, and dataacquisition using time averaging is nearly identical to ensembleaveraging. However, if the characteristic time of diffusion issubstantially longer than the time interval necessary for measuringfluorescence intensity (which is usually 10 to 50 μs), then activetransport (flow or scanning) can considerably save time of dataacquisition.

[0030] The measurement volumes can preferably be arranged ontwo-dimensional carriers, such as membranes or sheets having wells.Suitable carrier systems are e.g. described in WO 94/16313 (EVOTECBioSystems GmbH). The measurement volumes might also be arranged in alinear way, as e.g. in a capillary system.

[0031] In fluorescence studies, it may be advantageous to take measuresor reducing the background count rate, arising from Raman scattering inthe solute material and dark count rate of the detector, with respect tothe count rate per particle. In particular, it is in some casespreferred to use measurement volumes smaller than 100 μm³, morepreferably about 1 m³. Advantageously, the high signal to backgroundcount rate and the small optical measurement volume may be achieved byusing at least one microscope objective, preferably with a numericalaperture ≧0.9, in a confocal manner for both focussing an incident laserbeam and collecting radiation, preferably light, emitted, scatteredand/or reflected by units, preferably particles, in said samples. Aconfocal microscope set-up is preferably used which comprises at leastone microscope objective, a dichroic mirror, a pin-hole in the imageplane of said microscope objective, a detection means, a dataacquisition means, and optionally means for scanning and/or activelytransporting the sample. A suitable device is disclosed in WO 94/16313(EVOTEC BioSystems GmbH). In a preferred embodiment the pin-hole mightbe replaced by an appropriate detector, as it is also described in WO94/16313. It might further be preferred to choose a working distancebetween the microscope objective and the measurement volume in such away that background contributions are minimized. Preferably, the workingdistance should be smaller than 1000 μm.

[0032] In a preferred embodiment of the method, multiple photonexcitation is used to excite a particle. Multiple photon excitationmeans that the sum, difference or any combination of wave frequences oftwo, three or more photons is used for excitation of the secondaryemission of the sample which can be e.g. luminescence or second orderRaman scattering. Such an excitation scheme has an advantage in thesense that the excitation probability is not linearly dependent onexcitation intensity, but on the second or higher power. Thus, themultiple photon excitation is mostly limited to the volume of the laserfocus, whereas outside the laser focus no spurious excitation isgenerated. Appropriate laser sources of picosecond or subpicosecondpulses are well known to those of skill in the art. The presentinvention profits from such an excitation scheme in the sense that lessbackground is generated compared to single photon excitation, and thatthere is no pinhole necessary to restrict the measurement volume. Thus,the pinhole diameter and its imaging on the detector do not enter asmodelling parameters in the spatial brightness function any more.

[0033] In a further preferred embodiment, the measurement volume isrestricted by the use of elements of near field microscopy. These can beused for focussing the excitation radiation of the units, and/orcollecting the radiation emitted, scattered and/or reflected by theunits. Near field optical microscopy means here that the light passesthrough an aperture with at least one of its dimensions being smallerthan the wavelength of the light used and which is in direct contact tothe measurement volume. The aperture may consist of an opaque layer withat least one hole of said diameter or at least one slit of appropriatewidth and/or a tapered glass fiber or wave guide with a tip diameter ofsaid width, optionally coated with an opaque layer outside. A suitabledevice is disclosed in WO 96/13744 and in the German patent 44 38 391(EVOTEC BioSystems GmbH).

[0034] Another preferred embodiment combines near field opticalmicroscopy for the excitation light path, and conventional opticalmicroscopy for the emission light path, or vice versa. The presentinvention profits from such a realization in the sense that the size ofthe measurement volume is reduced compared to conventional confocalmicroscopy. Thus, the present invention can be used to measure higherparticle concentrations as with other optical schemes.

[0035] A sample is usually characterized by values of concentration andspecific brightness of one or more species of units, e.g. types offluorescent particles. In cases when one or more of these values areknown beforehand, the goal of analysis is to determine unknown values,either those of concentration, or specific brightness, or both.

[0036] Two alternative methods for selecting the model yielding a fitbetween the experimentally determined and calculated functions,preferably distributions of the number of photon counts can be used. Inone embodiment, the well-known least squares fitting method, where thesample is described by a finite (usually small) number of parameters,can be employed. The purpose is to find values of the parametersyielding the closest fit between the experimental and the calculatedcurves. According to the invention, values of concentrations and/orspecific brightnesses of a number of species of units, e.g. types offluorescent particles, can be estimated. In a further embodiment,another general method called inverse transformation with linearregularization (ITR) can be employed. ITR describes the sample using asemi-continuous distribution function of units, preferably particles,versus their specific brightness, and searches for the closest fitdemanding that the solution is a smooth function (For the method of ITR,see, e.g., W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P.Flannery, Numerical recipes in C: the art of scientific computing,second edition, Cambridge University Press, 1992, p. 808). It mightfurther be preferred to use an inverse transformation with constraints(ITC) or an inverse transformation with regularization and constraints(ITRC). Because of statistical errors and limited sizes of measureddata, inverse transformation is often an ill-posed mathematical problem,characterized by wild oscillations in its outcome. ITR, ITC and ITRCstabilize the mathematical problem by looking for a “regular” (e.g. asmooth) or constrained solution, for example by minimizing the sum ofsquared deviations of statistical data and a function of the solutionitself, penalizing “irregular”, usually irreproducible structures in theoutcome, or values having no physical meaning. An example forconstraining is disallowing negative values for concentration.

[0037] In the following, the invention is further illustrated in anon-limiting manner. Particularly, it is described how the expecteddistribution of the number of photon counts is determined.

[0038] A preferably many times repeated step in the calculation of theprobability distribution of the number of photon counts is calculationof the probability distribution of the number of photon counts emitted,scattered and/or reflected by single species from a spatial section ofthe measurement volume with a constant value of spatial brightness. Itis well known that the probability distribution of the number ofparticles in an open volume is Poissonian. Also, if the number ofparticles inside the spatial section is given, the number of detectedphotons per sampling time interval is Poisson distributed. Consequently,the overall distribution of the number of photon counts emitted,scattered and/or reflected by single species from a spatial section ofconstant brightness and detected by an ideal detector is compoundPoissonian.

[0039] As the next step, one may study the case in which the measurementvolume is divided into a number of spatial sections of constantbrightness. If the values of volumes and spatial brightnesses in each ofthe sections are known, the distribution of the number of photon countscorresponding to each section can be determined separately. All thesedistributions are compound Poissonian. Furthermore, if distributions ofthe number of photon counts for all sections were known, the overalldistribution can be determined through convolutions, using the fact thatthe total number of counts is the sum of the number of countsoriginating from different sections of the measurement volume.

[0040] As the following step, one may study a mixture of species, e.g.mixtures of fluorescent particles having different values of specificbrightness. Each spatial section of the measurement volume can bedivided into a number of abstract subsections each containing onlyparticles of a single species. A similar procedure can be applied now asdescribed above for spatial sections of the measurement volume in orderto determine the overall distribution of the number of photon counts.

[0041] An experimentally determined distribution of the number of photoncounts is ruled not only by properties of the light beam, but isinfluenced also by nonideal properties of the photon detector.Stochastically, the dark counts of the detector behave in the samemanner as photon counts from background light of constant intensity.Their contribution are photon counts of Poisson distribution. Also, theway how the dead time of the detector and its afterpulsing distort thedistribution of photon counts are known from literature on photonstatistics (see e.g. B. Saleh, Photoelectron Statistics, Springer,Berlin, 1978).

[0042] In summary, the expected distribution of the number of photoncounts is determined, from one side, by characteristics of the sample(concentrations and specific brightnesses of fluorescent particles ofdifferent kind), and, from the other side, by characteristics of theequipment (the sampling time interval, the spatial brightness function,the background count rate, the dead time and the afterpulsingprobability of the detector).

[0043] In one embodiment, both the dead time and the afterpulsingprobability of the detector are determined from experiments in which thedistribution of the number of photon counts corresponding to light ofconstant intensity is determined. Correction for the dead time of thedetector may be performed on the basis of a formula derived by Cantorand Teich (J. Opt. Soc. Am. 65, 786,1975; see also B. Saleh, p.272-277). Mathematics of afterpulsing is simple: each photon pulse canbe followed by another (artificial) pulse; this happens usually with aconstant probability.

[0044] According to the invention, it is preferred that the spatialbrightness function is characterized using experiments on a singlespecies of particles. For example, if the laser wave-length 514.5 nm isused, then a solution of Rhodamine 6G is a convenient sample which canbe used for characterizing the spatial brightness function.

[0045] What characteristics of the spatial brightness function can beemployed when determining the expected distribution of the number ofcounts are values of volumes of the sections of the measurement volumecorresponding to a selected set of values of the spatial brightness.Typically, a set of twenty or thirty values of the spatial brightnesspositioned at a constant distance from each other in the logarithmicscale have been selected, covering two or three orders of magnitude.Contribution from the lower brightness areas can be accounted for by asingle parameter, their relative contribution to fluorescence intensity.Intensity fluctuations of this light can be neglected. Because of thelarge number of the sections of the measurement volume, it would be lesspreferred to consider volumes corresponding to each of the sections asindependent variables. It is convenient to consider them as variablesdepending on a few other parameters, and determine the values of theseparameters which yield the closest fit between the experimentallydetermined and the calculated distribution of the number of photoncounts. Conveniently, a relatively simple model of the optical set-up isapplied, which is not accounting for aberrations of the optics used, andwhich determines volumes of the sections of the measurement volume. Forinstance, the volumes of the sections depend on values of theconvergence angle of the laser beam and the diameter of the pinhole. Itmight therefore be preferred to use the pinhole dimensions and theconvergence angle of the incident laser beam as modelling parameters ofthe spatial brightness function.

[0046] Alternatively, simple mathematical expressions with formalparameters can be used instead of physical models for determining thevolumes of spatial sections. The values of the formal parameters shouldpreferably be selected in such a way that the closest fit betweenexperimental and calculated distributions of the number of photon countsis achieved. Formal flexible expressions are advantageous because theyyield a good fit between experimental and theoretical distributions ofthe number of photon counts. Secondly, calculations based on simplemathematical expressions are very fast compared to those based onphysical models.

[0047] According to the invention, it may in some cases be preferred toselect the length of the sampling time interval in such a way that inaverage more than one, preferably one to ten, counts per unit areyielded.

[0048] It may further be preferred that the length of the time intervalis in average smaller than the characteristic correlation time ofradiation intensity fluctuations.

[0049] If more than two unknown parameters of the sample have to beestimated, it is preferred to have no more than a few, preferably aboutone unit, preferably particle, per measurement volume.

[0050] It is preferred to have less than 10 units per measurementvolumes to obtain good signal-to-noise ratios.

[0051] In one embodiment, at least one individual unit is statisticallyanalyzed in terms of its specific brightness which may fluctuate orchange non-stochastically.

[0052] The method of the present invention is particularly advantageousbecause information losses and distortions are kept minimal.Furthermore, a new quality attainable by the present invention is thatthe data processing depends less on a definite mathematical model of thesample compared to the other techniques which are state of the art. Thismeans that the method is more reliable in terms of long term stabilityof an instrumental realization, and that any disturbation of themeasurement volume by e.g. turbid samples or particles inside he laserbeam does not significantly influence experimental results.

[0053] A further new quality attainable by the present invention is thatthe signal-to-noise ratio is much better compared to the techniques ofthe prior art. This means that experiments can be made withinsignificantly shorter time (up to 100 fold shorter) than previously,showing the same signal-to-noise ratio as previous long termexperiments. Since photo-bleaching of fluorescent molecules orfluorescently labelled molecules is an unsolved problem so far with anyapplied measurement technique in this field, especially when applied tocells, one is restricted to short measurement times. Thus, compared tothe prior art, the present invention is advantageous for measurementsinside cellular systems.

[0054] In one preferred embodiment, the present invention is realized inthe field of fluorescence intensity fluctuation studies. The opticalequipment is a conventional confocal FCS microscope equipped with a cwlaser of visible light. The excitation laser beam is focussed into asample which is a homogeneous water solution of a low concentration,typically in the nanomolar range, of fluorescent material. Fluorescenceemission from a microscopic confocal volume of about 1 μm³ is collectedon a photon detector. The measurement time which is typically 1 to 60seconds is divided into hundreds of thousands time intervals of typicalwidth of 10 to 50 μs. The highest number of photon counts typicallyobtained in this experimental realization of the invention hereindescribed is between 10 and 100.

[0055] The method according to the present invention is particularlywell suited for use in high throughput screening, diagnostics,monitoring of polymerization, aggregation and degradation processes, oranalytics of nucleic acids.

[0056] In screening procedures, substances that are possiblypharmacologically active can be analyzed through their interaction withspecific receptors by examining said interaction with binding of aluminescently labelled ligand to receptors wherein natural receptors ontheir carrier cells as well as receptors on receptor-overexpressingcarrier cells or receptors on vesicles or receptors in the form ofexpressed molecules or molecular complexes may be used. Moreover, theinteraction of substances with enzymes in solution or in their genuinecellular environment can be detected by monitoring a change of thesubstrate of the enzyme, e.g. a change in brightness. Furtherapplications, especially concerning the performance of assays, aredisclosed in WO 94/16313 (EVOTEC BioSystems GmbH).

[0057] For the detection of specific recognition reactions, potentialactive substances can be present in complex natural, synthetic orsemisynthetic mixtures which are subjected to separation prior toanalysis. These mixtures can be separated first e.g. by chromatographyto test the individual fractions for the presence of functionalcompounds preferably “on line” in a capillary at the end of a separationmatrix. The coupling of fractionating methods with FCS detection isdescribed in detail in WO 94/16313 (EVOTEC BioSystems GmbH). A similarset-up can be used with respect to the present invention.

[0058] Often, aggregation and degradation are phenomena to be monitored.Aggregates display brightnesses different from the monomers and can bemonitored according to the present invention.

[0059] In sequencing according to the method of Sanger, oligomers ofdifferent length, of which the terminating nucleic acid is labeled witha dye, are identified. Advanced techniques, as e.g. the one described inDE 38 07 975 A1, use dyes which exhibit different properties, such asfluorescence lifetime, according to the type of base they are attachedto. The determination of a base is much more secure if severalproperties, such as fluorescence lifetime and brightness, or any otherspecific physical property, are determined and cross checked forconsistency. In a preferred embodiment, the sample to be sequenced isseparated by gel or capillary electrophoresis, or a separation step isconducted by capillary electro-chromatography, elecrohydrodynamicmigration or related electrokinetic methods.

[0060] EXAMPLE 1

[0061] The nature and advantages of the invention may be betterunderstood on the basis of the following example where a mixture ofrhodamine dyes is analyzed. FIGS. 1 to 7 illustrate consecutive steps ofthe analysis and their results.

[0062]FIG. 1. Distributions of the number of photon countsexperimentally determined at constant light intensities, time intervalof 10 μs and data collection time of 50 s. From curve fitting, the deadtime of the detector was estimated to be 28±4 ns; afterpulsingprobability 0.0032±0.0008. In the lower graph, weighted residuals of thecurve fitting are presented.

[0063]FIG. 2. Distribution of the number of photon counts experimentallydetermined for a solution of rhodamine 6G at time interval of 40 μs anddata collection time of 50 s.

[0064]FIG. 3. Normalized sizes of volumes of the twenty spatial sectionsof the measurement volume of the highest brightness. Section 0corresponds to the maximal value of the spatial brightness while section19 corresponds to about 100 times lower brightness. Sizes of volumes aredetermined from experiments on single fluorescent species.

[0065]FIG. 4. Residuals of curve fitting corresponding to an experimenton rhodamine 6G solution (the experiment graphed by FIG. 2).

[0066]FIG. 5. Distribution of the number of photon counts experimentallydetermined for three samples at time interval of 40 μs and datacollection time of 50 s. The distribution corresponding to rhodamine 6Gis the same as in FIG. 2.

[0067]FIG. 6. The results of the inverse transformation with linearregularization applied to the data of FIG. 5.

[0068]FIG. 7. Residuals corresponding to analysis of an experiment onthe mixture solution of rhodamine 6G and tetramethylrhodamine (measureddata in FIG. 5). Graph a: expected curve was obtained by inversetransformation with linear regularization. Graph b: expected curve wasobtained by the least squares fitting of the experimental data. Graph c:residuals of the least squares curve fitting under a wrong assumption ofsingle species.

[0069] As the first preparatory step of analysis, the dead time and theafterpulsing probability of the photon detector are estimated. This wasdone by determining the distribution of the number of photon countsunder illumination of the detector by light of constant intensity. Sincethe dead time distortions are most noticeable at high count rates whilethe afterpulsing distortions are better resolved at low count rates, thevalues of the dead time and the probability of afterpulsing weredetermined by jointly fitting distributions of the number of photoncounts determined at a relatively high and ad a relatively lowillumination intensity. The experimentally determined count numberdistributions are presented in FIG. 1, together with residuals of thecurve fitting. Values of the estimated parameters for the photondetector which have been used are: dead time 28 ns, afterpulsingprobability 0.003.

[0070] The background count rate of the equipment is determined bymeasuring the count rate when the sample holder is filled with purewater.

[0071] As the second preparatory step, the spatial brightnessdistribution corresponding to a given optical set-up, was characterized.For that purpose, the distribution of the number of photon countscorresponding to a solution of rhodamine 6G was experimentallydetermined (FIG. 2). If the spatial brightness distribution isappropriately characterized, then the calculated curve fits theexperimental curve. In order to numerically calculate the expecteddistribution of the number of photon counts, values of twenty oneparameters characterizing the spatial profile are needed in our program:twenty sizes of volumes corresponding to twenty spatial sections of thehighest values of spatial brightness, and the relative contribution tofluorescence light originating from areas of lower spatial brightness.In order to calculate values of these unknown parameters, a simple modelof the optical equipment not accounting for aberrations was taken intouse. As illustrated by FIG. 3, the determined sizes of the twentyvolumes are reproducible, even if other species than rhodamine 6G areused.

[0072] Having determined values of the twenty one parameterscharacterizing the spatial brightness distribution in the way justdescribed above, the calculated distribution of the number of photoncounts indeed fits the experimentally curve, see FIG. 4.

[0073] After the preparatory steps described above the equipment isready for analysis. In FIG. 5, distributions of the number of photoncounts corresponding to three different samples are presented. In FIG.6, the results of the inverse transformation with linear regularizationare graphed. Both spectra corresponding to single species (rhodamine 6Gor tetramethylrhodamine) have a single peak, but the peaks are centeredat different values of specific brightness. The peak of rhodamine 6G issituated at about 108 kHz/molecule, whereas the peak oftetramethylrhodamine is centered at about 37 kHz/molecule. Thisindicates that a rhodamine 6G molecule is about 3 times brighter than atetramethylrhodamine molecule. The spectrum corresponding to the mixtureof the two species has two peaks centered indeed near the valuesobtained for the two species separately.

[0074]FIG. 7 illustrates the residuals corresponding to the measurementsof the mixture of rhodamine 6G and tetramethylrhodamine. Differentmethods of data processing yield slightly different fit curves (anddifferent residuals). The upper graph corresponds to the spectrum ofspecific brightness obtained by inverse transformation with linearregularization. The middle graph corresponds to the fit curve obtainedassuming two species. These two graphs are nearly identical. Theexperimentally determined distribution of the number of photon countscan formally be fitted under the wrong assumption of single species,which is shown in the lower graph, but the fit curve is obviously apartfrom the experimental one.

[0075] EXAMPLE 2

[0076] To further demonstrate the usefulness of the present invention, ahybridization process was studied using a conventional confocal FCSmicroscope. A model system based on the interaction of two 32-baseoligonucleotides, both labelled with the fluorescent dye TAMRA (5- (and6-) carboxytetramethylrhodamine), has been investigated. The sequence ofthese oligonucleotides included a site for the restriction enzyme EcoRIenabling the cleavage of the primer dimer. This restriction analysis wasused as a control in order check the specificity of the results obtainedby the method according to the present invention.

[0077] The hybridization was performed in a 10 mM Tris buffer (pH 7.4)containing 1 mM EDTA and 100 mM NaCl, the restriction analysis in 50 mMTris-HCl (pH 7.5), 10 mM MgCl₂, 100 mM NaCl, 0.2% Triton X-100. Themeasurement time for each analysis was 30 seconds.

[0078]FIG. 8. Number of particles per volume element as a function oftheir specific brightnesses.

[0079] The analysis of the TAMRA-labelled single-strand oligonucleotidesrevealed a single characteristic fluorescence intensity peak of 45 kHzfor oligonucleotide A (FIG. 8a), and of 20 kHz for oligonucleotide B(FIG. 8b) upon excitation at 543 nm.

[0080] The hybridization of the oligonucleotides A and B resulted in asingle intensity peak of 35 kHz (FIG. 8c) indicating that thehybridization was complete. From the intensity values of the individualoligonucleotides, one would have expected an intensity peak of 65 kHzfor this primer dimer. This discrepancy in the intensity can beexplained by the occurrence of dye-nucleotide interactions and electrontransfer-induced quenching.

[0081] Further evidence that the 35 kHz intensity peak represents theprimer dimer is given by an cleavage experiment using EcoRI (FIG. 8d).Restriction cleavage of the annealed primers results in an intensitypeak of 20 kHz. The broadening of the intensity distribution indicatesthat the reaction was not complete.

[0082] These experiments demonstrate that the method according to thepresent invention is well-suited for studying hybridization processeswhich play an important role for the detection and characterization ofpathogens. The ability of the method according to the present inventionto measure the activity of a restriction endonuclease was alsodemonstrated by this series of experiments.

[0083] EXAMPLE 3

[0084] Biotin labelled with the following different dyes

[0085] a) 5- (and 6-) carboxy-X-rhodamine (abbr. ROX)

[0086] b) 5- (and 6-) carboxytetramethylrhodamine (abbr. TAMRA)

[0087] c) Rhodol Green™

[0088] d) Rhodamin Green™

[0089] e) Resorufine

[0090] f) Texas Red and

[0091] g) Rhodamine B

[0092] with and without a spacer molecule (abbr. Sp.) as well as theirmixtures with streptavidin have been analyzed according to the method ofthe present invention in order to monitor quenching effects ofdifferently labelled biotin upon streptavidin binding.

[0093]FIG. 9 shows the specific brightnesses of the different molecules.The presence of streptavidin is indicated by “+”, whereas its absence isindicated by “−”.

[0094] EXAMPLE 4

[0095] The following example proves that the method according to thepresent invention is valid for the measurement of ligands bound toreceptor populations on membrane vesicles.

[0096] The use of crude biological material such as biomembranes derivedfrom tissue or cells in assays to be analyzed by single particlefluorescence detection analysis brings along issues dealing with thenature and heterogeneity of this material. When membrane preparationsare generated from receptor-overexpressing cells, the most probablesituation will be that there are many receptor molecules on a singlemembrane vesicle. For an analysis of fluorescent ligand binding to thosereceptors, the method according to the present invention is ideallysuited because it discriminates between particles which displaydifferent fluorescence intensities. Membrane vesicles are slowly movingparticles (mean diffusion time T_(diff)>10 ms) in a low concentration.Thus to attain a reasonable signal-to-noise ratio, the measurement timesfor these rare events have to be prolonged compared to nanomolarfluorophore solutions. In order to shorten measurement time and improvestatistical accuracy, the effective volume to be analyzed had to beincreased substantially without loosing the advantage of detectingsingle molecules. This has been achieved by introducing a beam scanningdevice. Using a beam scanner also circumvents bleaching effects sincethe mean excitation time of a single vesicle is minimized by themovement of the laser beam.

[0097] The feasibility to quantify a biological interaction by themethod according to the present invention as demonstrated usingepidermal growth factor (abbr. EGF) binding to membrane vesicles fromA431 human carcinoma cells. These cells express 10⁵ to 10⁶ epidermalgrowth factor receptors per cell.

[0098] Membrane vesicle preparations

[0099] Membrane preparations were carried out by cell disruption in ahypotonic buffer (20 mM Tris/HCl, pH 7.5, 5 mM MgCl₂) containingprotease inhibitors (leupeptin, aprotinin and PMSF) using a glasshomogenizer and high-spin centrifugation after removal of nuclei at lowg force. 10% sucrose was added during the first centrifugation step. Themembranes were homogenized in EGF binding buffer (20 mM HEPES pH 7.4,140 mM NaCl, 5 mM MgCl₂, 1.8 mM CaCl, 4.2 mM NaHCO₃ and 5.5 mM glucose)using a Branson sonifyer prior to the experiment. Protein content wasdetermined with bicinchoninic acid (PIERCE) to 0.504 mg/ml (A431).

[0100] EGF binding studies

[0101] Binding experiments using EGF labelled with tetramethylrhodamine(abbr. TMR) and A431 membranes were performed according to Carraway etal. (J. Biol. Chem. 264:8699,1989). Briefly, they were diluted with EGFbinding buffer and were incubated with labelled ligand in 20 μl samplesfor 40 minutes at room temperature. In competition experiments,membranes were incubated with unlabelled EGF. Measurements of 30 secondsduration were carried out using one-dimensional beam scanning at 25 Hzand an amplitude of 700 μm.

[0102]FIG. 10 shows a plot of the amount of ligand-receptor complexes inrelation to the total ligand concentration.

[0103]FIG. 11 shows examples of intensity distributions measured atcertain concentrations of A431 vesicles.

[0104] The y-axis of the intensity distributions in FIG. 11 isconstructed by multiplying the particle number obtained for eachintensity in the grid of intensities by the intensity of that gridpoint, thus representing the contribution of particles at that intensityto the total intensity. It is preferred to choose this transformation asit emphasizes on particles with high intensity, but low concentrationwhich is the case for vesicles with bound ligand. In terms of particlenumbers (concentration), vesicles would only make a negligiblecontribution.

[0105]FIG. 11a shows the intensity distribution of the ligand alone. Theligand has an intensity of about 40 kHz/particle. In FIGS. 11 b-d,intensity distributions with increasing concentrations of vesicles areplotted. The increase of fluorescence from bright particles, i.e.vesicles with many ligand-receptor complexes on them, is clearlyvisible.

[0106] In order to quantify the degree of binding, one has todistinguish between unbound ligand and ligand-receptor complexes.Vesicles with several bound ligands are brighter than the ligand alone.Thus, a certain discriminating intensity I_(d) is chosen. Particlesdetected below this intensity are assumed to be ligand molecules, whileparticles detected above this intensity are counted as vesicles withreceptor-ligand complexes.

[0107] The concentration c_(L) of free ligand is determined by summingup over all concentrations below the discriminating intensity:$c_{L} = {\sum\limits_{\forall{i:\quad {l_{i} < l_{d}}}}c_{i}}$

[0108] The concentration C_(RL) ligand-receptor complexes is given bythe assumption that a vesicle with n bound ligands has an intensity of ntimes the ligand intensity. Thus, an intensity component at an intensityI is from a vesicle with n=I/I_(Ligand) ligand-receptor complexes, andthe concentration of these complexes is given by$c_{RL} = {\sum\limits_{\forall{i:\quad {l_{i} \geq \quad l_{d}}}}{c_{i}\frac{l_{i}}{l_{Ligand}}}}$

[0109] Now, the degree of complex formation is given by${complex} = \frac{c_{RL}}{c_{L} + c_{RL}}$

[0110] This is plotted in FIG. 10 for the binding of labelled EGF toA431 vesicles.

1. A method for characterizing samples having units, by monitoringfluctuating intensities of radiation emitted, scattered and/or reflectedby said units in at least one measurement volume, the monitoring beingperformed by at least one detection means, said method comprising thesteps of: a) measuring in a repetitive mode a number of photon countsper time interval of defined length, b) determining a function of thenumber of photon counts per said time interval, c) determining afunction of specific brightness of said units on basis of said functionof the number of photon counts.
 2. A method according to claim 1,wherein said function of the number of photon counts per said timeinterval and/or said function of specific brightness is a distributionfunction.
 3. The method according to claim 1 and/or 2, wherein saidunits are molecules, macromolecules, dyes, molecular aggregates,complexes, vesicles, cells, viruses, bacteria, beads, centers, ormixtures thereof in solids, liquids or gases.
 4. The method according toat least one of the claims 1 to 3, wherein said units can be groupedinto species which can be distinguished by their specific brightness. 5.A method according to at least one of the claims 1 to 4, wherein atleast one species is luminescent, preferably fluorescent, and/or isluminescently labelled.
 6. A method according to at least one of theclaims 1 to 5, wherein the luminescence properties of the units arevaried by conjugating them with a first molecule, in particular biotin,which binds a luminescently labelled second molecule, in particularluminescently labelled avidin or streptavidin, or vice versa.
 7. Amethod according to claim 6 wherein the first molecule is a (6xHis)tagand the second molecule is a luminescently labelled Ni-NTA-derivatives.8. A method according to at least one of the claims 1 to 7, wherein theluminescence properties of a unit are changed by energy transfer, inwhich energy absorbed by said unit is transferred upon close contact toa luminophore of an acceptor and subsequently emitted.
 9. A methodaccording to at least one of the claims 1 to 8, wherein said units eachcarry a number of binding sites for luminescent units.
 10. A methodaccording to at least one of the claims 1 to 9, wherein the measurementvolume is only a part of the total volume of the sample and has a volume≦10⁻¹² l, preferably ≦10⁻¹⁴ l.
 11. A method according to at least one ofthe claims 1 to 10, wherein said units are diffusing and/or beingactively transported into and out of said measurement volume and/or thesample is actively transported and/or optically scanned.
 12. A methodaccording to at least one of the claims 1 to 11, wherein the measurementvolumes are arranged on a two-dimensional carrier, in particular or amembrane or in sheets having wells, or in linear way, preferably in acapillary system.
 13. A method according to at least one of the claims 1to 12, wherein a confocal microscope set-up is used, comprising at leastone microscope objective, preferably with a numerical aperture ≧0.9, forboth focussing an incident laser beam and collecting radiation emitted,scattered and/or reflected by said units of said sample, a dichroicmirror, a pin-hole in the image plane of said microscope objective, adetection means, a data acquisition means, and optionally means forscanning and/or actively transporting said sample.
 14. A methodaccording to at least one of the claims 1 to 13, wherein saidmeasurement volume is restricted by the use of elements of near fieldoptical microscopy, or their combination with conventional microscopyoptics.
 15. A method according to at least one of the claims 1 to 14,wherein fluorescence is induced using multiple photon excitation.
 16. Amethod according to at least one of the claims 1 to 15, wherein theparameters of a spatial brightness function characteristic for theoptical set-up are determined by measuring numbers of photon counts perdefined time intervals in a repetitive mode from radiation emitted,scattered and/ or reflected by a single species.
 17. A method accordingto at least one of the claims 1 to 16, wherein the dimension andtwo-dimensional shape of the pinhole positioned in the focal plane ofthe microscope is used as a modelling parameter of the spatialbrightness function.
 18. A method according to at least one of theclaims 1 to 17, wherein the convergence angle or the incident laser beamis used as a modelling parameter of the spatial brightness function. 19.A method according to at least one of the claims 1 to 18, wherein theconcentration and/or specific brightness of at least one species of saidunits is determined.
 20. A method according to at least one of theclaims 1 to 19, wherein said distribution of the number of photon countsis fitted using a priori information on the sample.
 21. A methodaccording to at least one of the claims 1 to 20, wherein saiddistribution of the number of photon counts is processed by applying aninverse transformation with linear regularization and/or constraints.22. A method according to at least one of the claims 1 to 21, whereinthe experimental parameters of the detection means, in particular deadtime and afterpulsing probability of the detection means, are determinedby measuring number of photon counts per defined time interval in arepetitive mode while the detection means is exposed to light ofconstant intensity or high frequency laser pulses.
 23. A methodaccording to at least one of the claims 1 to 22, wherein backgroundcount rate of the equipment is determined.
 24. A method according to atleast one of the claims 1 to 23, wherein the length of said timeinterval is in average smaller than the characteristic correlation timeof radiation intensity fluctuations.
 25. A method according to at leastone of the claims 1 to 24, wherein the length of said time interval isselected to yield in average more than one, preferably one to ten,photon counts per said unit.
 26. A method according to at least one ofthe claims 1 to 25, wherein the concentration of the sample or the sizeof the measuring volume is selected to have in average no more than afew, preferably about one unit per measurement volume.
 27. A methodaccording to at least one of the claims 1 to 26, wherein at least oneindividual unit is statistically analyzed in terms of its specificbrightness which may fluctuate or change non-stochastically.
 28. Amethod according to at least one of the claims 1 to 27 for use in highthroughput screening, diagnostics, monitoring of polymerization,aggregation and degradation processes, or analytics of nucleic acids.